Please continue blogging about your work, it is most interesting!

Cheers,

T.

Thank you a lot for your post on your blog http://dorigo.wordpress.com/2009/01/04/what-is-a-glueball/ and the comment about this post. The question runs as follows and is strongly rooted in the work I have done in the latest three years. It is also something that seems quite simple in view of the work condensed matter theorists have been doing since the seminal papers by Landau.

When one considers the Hamiltonian of a solid one general meets difficulties to describe its properties unless the proper states to build perturbation theory are given. These states are known as quasiparticles or dressed particles. After the proper choice is done you can work out perturbation theory and so, a lot of results come down for metals and other materials after this understanding come out. Today, this approach is quite generally accepted in condensed matter physics and has had as a by-product the understanding of superconductivity through BCS theory and Cooper pairs as fundamental states of the Hamiltonian.

For a Yang-Mills theory in the infrared limit you are in a similar situation. At higher energies asymptotic freedom sets in. This mean that you are able to apply small perturbation theory and the states to work with are those of a free theory: Gluons with all their well-known properties as also seen in high energy experiments. But when the coupling in the theory becomes too large the non-linear terms cannot be neglected anymore and you are exactly in the situation of Landau trying to understand why Fermi theory of free electrons appears so good at describing the properties of metals, while these particles should be strongly bounded inside the material.

Indeed, a class of exact classical solutions of Yang-Mills theory exist having a very nice property. They can be represented in quantum field theory with a Gaussian functional and the spectrum of an harmonic oscillator. Ooops! Quasiparticles? Like condensed matter theory?!! This is all the matter since now. The papers you should look at are the following

http://arxiv.org/abs/0807.2179

This gives the classical solutions but the part of QFT is wrong. I have to correct it and I will do it in the due time.

http://arxiv.org/abs/0812.0934

This paper gives a fully QCD computation of the resonance width and an understanding of observability of pure Yang-Mills spectrum in high-energy experiments.

http://arxiv.org/abs/0709.2042

This has been published (see http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVN-4TPHRKP-3&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=fd5ae79f41aeba1b0ebab2efa65bf73a) and gives a full mathematical account of all this matter.

A full report of all this view is given in

http://arxiv.org/abs/0807.4299

This is the result of my talk at QCD 08 in Montpellier in France. It will appear shortly in the proceedings. Very nice conference. You can look at some of my posts about as https://marcofrasca.wordpress.com/2008/07/14/qcd-08-the-report/

Ciao,

Marco

]]>Cheers,

T.